1
A Brief Primer on Social Network Analysis
Daniel J. Brass and Stephen P. Borgatti
We are extremely pleased to offer this edited volume on Social Networks at Work. We have assembled an outstanding group of authors who have provided their latest thinking on social networks as they apply to industrial/organizational (I/O) psychology. We begin with a brief primer on social network analysis, designed for those considering adding a social network perspective to their I/O research, and preview some of the network concepts found in the following chapters. Each chapter represents a stand-alone contribution, and can be read in any order, although we have organized them into two groups. The first group, Chapters 2â7, focuses on a particular network concept (centrality, affect, negative ties, multiplexity, cognition, and structural holes) applied across a variety of industrial/organizational topics. In contrast, the second group, Chapters 8â16, focuses on a particular industrial/organizational topic (personality, creativity, turnover, careers, personâenvironment fit, employment, teams, leadership, and culture) from a network perspective, applying a variety of network concepts to the topic.
Several excellent reviews of social network analysis exist (Borgatti, Mehra, Brass, & Labianca, 2009; Brass, Galaskiewicz, Greve, & Tsui, 2004; Burt, Kilduff, & Tasselli, 2013), which we will not repeat. We refer you to Kilduff and Brass (2010) for core ideas and debates; Borgatti and Halgin (2011) for network theories; Borgatti, Brass, and Halgin (2014) for confusions, criticisms, and controversies; and Brass (2012) for a review of fundamentals and a glossary of measures. For a comprehensive volume on analysis, see Borgatti, Everett, and Johnson (2018); for egocentric networks, see Perry, Pescosolido, and Borgatti (2018). We begin with some basic concepts and definitions.
A network is a set of nodes together with a set of ties representing some kind of connection between pairs of nodes. Often, multiple kinds of ties are collected (such as friendship ties, collaboration ties, conflicts, and so on), and these are typically analyzed separately so that each type of tie forms its own network. In the social sciences, the nodes typically represent agentic actorsâsuch as individuals, groups, and organizationsâthat are capable of forming or cutting ties. In other fields, nodes may include passive elements such as books or traffic intersections. Actors can be connected on the basis of (a) similarities (same location, membership in the same group, or similar attributes such as gender); (b) social relations (kinship, roles, affective relations such as friendship, or cognitive relations such as âknows aboutâ); (c) interactions (talks with, gives advice to, demeans); or (d) flows of goods or information (Borgatti et al. 2009). Of course, a given pair of actors may be connected in multiple ways, referred to as multiplexity. As Borgatti and Halgin (2011, p. 1170) note, different types of connections yield different types of networks. Every network question generates its own network. The choice will depend on oneâs research question. In organizational research, the links typically involve (a) some form of interaction or transaction, such as communicating with, giving advice or selling something to, or (b) represent a more abstract relational state, such as trust, friendship, or influence. Recent attention has focused on negative ties as well as positive or neutral ties (Labianca & Brass, 2006). We refer to a focal actor in a network as ego; the other actors with whom ego has direct relationships are called alters.
To collect social network data is to capture the presence/absence (or strength) of ties among pairs of actors. These dyadic relationships can be obtained from archival data (i.e., organizational alliances or email records), observation (i.e., the bank-wiring room in the famous Hawthorne studies), interviews, or respondent reports. In addition, there are social media data such as Twitter following and Twitter retweeting. At the individual level, the most common method is a questionnaire asking respondents to indicate who they have ties with, either by selecting them from a roster of names or listing names in an open-ended format. Network questions can be easily combined with more traditional questions that focus on attributes of the respondents, such as their attitudes or demographic characteristics.
Typical social science research data are entered into an actor-by-variable data matrix for analysis; actor rows by variable columns, with each cell representing the value of a variable for a particular actor. However, social network data capture relationships and are canonically entered into a square, actor-by-actor matrix X where each cell (i,j) represents the presence or absence or strength of a connection between actors i and j.1 Thus, ties may be binary or valued (i.e., 1â7 on a Likert-type scale to indicate frequency or intensity). Ties may also be entered to indicate direction such as resources flowing from Actor A to Actor B, or Actor A chooses Actor B as a friend, while some types of ties are inherently symmetric or bidirectional. Ties may also represent physical proximity or affiliations in groups, or events, such as chief executive officers (CEOs) who sit on the same boards of directors (e.g., Mizruchi, 1996). In this case, ties are entered into an actor-by-affiliation matrix and can be converted to an actor-by-actor matrix where each cell represents the number of common affiliations between the two actors, or an affiliation-by-affiliation matrix where each cell represents the number of common actors shared by the two affiliations (such as two groups or two events).
While these dyadic relationships are the basic building blocks of networks, the unique contribution of the network perspective is that it goes beyond the dyad and provides a way of considering the paths of connections and the structural arrangement of many actors (Brass, 2012; Borgatti et al., 2018). Typically, a minimum of two links connecting three actors is implicitly assumed in order to establish such notions as indirect linkages or paths. For example, Travers and Milgram (1969) traced the path lengths of volunteers attempting to reach a target person, resulting in the well-known âsix degrees of separationâ and subsequent âsmall-worldâ research (c.f., Watts, 2003). Just as actors are not considered in isolation, neither are dyadic relationships; it is the connections among the dyadic building blocks that form the network.
An extensive variety of network measures have been developed over the years (see Brass, 2012 for a glossary), as social network researchers have examined how the pattern of connections among actors affects various outcomes. Such measures are often referred to as âstructuralâ in that their values are based solely on the structure or configuration of relationships among the actors. These structural measures can be further classified as âpointâ measures when they describe an actorâs position within a network and âwholeâ network measures when they describe the configuration of the entire network (or some subnetwork within it). For example, an actorâs point centrality within a network can be captured in a number of ways (i.e., degree: number of ties; closeness: the minimum number of direct and indirect ties needed to reach every other actor in the network; or betweenness: the extent to which the actor falls on the shortest path connecting other pairs of actors in the network). A frequently calculated whole network measure is density; the number of actual ties divided by the total number of possible ties in the network.
Whole network data are collected by designating a bounded group of actors (such as a department or an organization) and collecting relational data among all the actors within the group (c.f., Brass, 1984). The challenge for the researcher is to bound the network so as to include all relevant actors (given the research question) and exclude irrelevant ones. When collecting whole network data, a general rule of thumb is that a response rate of more than 80% tends to capture the important features of the network. Whole networks are sometimes described as âsmall worldâ or clique structures in which we find tightly connected clusters of actors with a few bridging ties that connect the clusters, or coreâperiphery structures in which a few actors are connected at the core and peripheral actors are connected to the core but not to each other.
Network concepts and measures have also been developed to identify groups. For example, a clique is a maximal set of actors where every actor is connected to every other actor (here, âmaximalâ means that if an additional node exists that is connected to every node in the clique, it must be included in that set in order for it to be called a clique). An n-clique is a maximal set of nodes in which every node is linked to every other by a path of length n or less. Obviously, a 1-clique is just a clique. A 2-clique is a looser group in which nodes need not be directly connected to every other, but also canât be more than two links away from each other. Similarly, a k-plex is a maximal set of actors in which each actor must be connected to at least nâk other members of the plex (where n is the size of the plex), which is to say, they can miss connecting with no more than k other members.
In addition, a set of egocentric or âego networkâ measures have been developed to characterize a focal actorâs pattern of direct ties. An ego network contains only the focal actor egoâs direct ties to alters, and any ties between the alters. An ego network may be extracted for each node in whole network data, but may also be constructed by surveying independent focal actors (see Perry et al., 2018 for a more detailed explanation of egocentric research designs).
A distinction is sometimes made between perceived and âactualâ networks. For example, Krackhardt and Porter (1985) argued that perceived connections between employees who quit an organization and those who stayed were a more appropriate predictor of âstayersâ satisfaction than âactualâ connections. In addition, Kilduff and Krackhardt (1994) showed that audience perceptions of connections to high status others were a better predictor of perceived performance than actual connections (actual connections were measured as corroborated agreement between specified respondents). Thus, cognitive representations of networks, or networks as âprismsâ as well as âpipes,â have been the focus of network studies (Podolny, 2001).
Smith, Menon, and Thompson (2012, p. 68) provide a useful classification for thinking about an actorâs ties. They refer to the potential network as all the ties that actors have, including dormant ties (past connections that have fallen into disuse and may not readily come to mind unless prompted; see Levin, Walter, and Murnighan, 2011). The activated network is a subset of all ties that âcome to mindâ in a particular situation, or when prompted by a particular research question. The mobilized network is the subset of the activated network that the focal actor actually interacts with in responding to a situation (although this will also depend on whether the alter is willing to interact).
This classification raises the question of whether ties, once formed, ever die. A cognitive perspective might suggest that ties remain as long as an actorâs memory of the tie remains. If ties are inherently reciprocal, memory may be required of both parties. In contrast, a perspective in which ties are viewed as real, independent of actorsâ perceptions, a tie may cease to exist when either party chooses to discontinue the connection. Of course, the type of ties, or the content of the connection, will affect decay (i.e., kinship ties are forever). Burt (2002) has noted that bridging ties (to disconnected others) decay quickly, while Krackhardt (1998) has shown that Simmelian ties (where two actors are reciprocally connected to one another and each is reciprocally connected to the same third party) are long-lasting. Krackhardt notes that when a tie is embedded in a clique, the presence of third parties mitigates the pursuit of individualsâ self-interests, reduces the bargaining power of single individuals, and facilitates cooperation and conflict resolution.
Thus, social network researchers are faced with several design questions as they seek to supplement the traditional focus on attributes with a relational, social network approach. If I am studying interactions, should I rely on self-report, or use archival records or observations? Freeman, Romney, and Freeman (1987) have shown that while informants are not very accurate about specific times or events, they are accurate in reporting recurrent, everyday connections. What type of ties should I focus on? Should I collect data on more than one type of network (i.e., friendship and advice)? Should I treat the ties as binary (present or absent) or collect valued data on the frequency or strength of the ties? Should I collect ego network data on the assumption that indirect connections (i.e., ...